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Additive Properties of the generalized and pseudo n-strong Drazin Inverse in Banach Algebras

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  • Rounak Biswas

    (National Institute of Technology Karnataka)

  • Falguni Roy

    (National Institute of Technology Karnataka)

Abstract

In this paper, we establish some necessary and sufficient conditions for generalized n-strong Drazin invertibility (gns-invertibility) and pseudo n-strong Drazin invertibility (pns-invertibility) of an element in a Banach algebra for $$n\in {\mathbb {N}}$$ n ∈ N . Subsequently, these results are utilized to prove some additive properties of gns (pns)-Drazin inverse. This process produces a generalization of some recent results of H Chen, M Sheibani (Linear and Multilinear Algebra 70.1 (2022): 53-65) for gns and pns-Drazin inverse.

Suggested Citation

  • Rounak Biswas & Falguni Roy, 2025. "Additive Properties of the generalized and pseudo n-strong Drazin Inverse in Banach Algebras," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(3), pages 917-929, September.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:3:d:10.1007_s13226-025-00811-8
    DOI: 10.1007/s13226-025-00811-8
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    References listed on IDEAS

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    1. Mosić, Dijana, 2016. "Reverse order laws for the generalized strong Drazin inverses," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 37-46.
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